Triangle read by rows: T(n,k) = number of colored weighted Motzkin paths ending at (n,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =9a(4) =2a(5) =1a(6) =25a(7) =15a(8) =3a(9) =1a(10) =145a(11) =52a(12) =22a(13) =4a(14) =1a(15) =561a(16) =285a(17) =90a(18) =30a(19) =5a(20) =1a(21) =2841a(22) =1206a(23) =495a(24) =140a(25) =39a(26) =6a(27) =1a(28) =12489a(29) =6027